\section{Experimental Results}
In this section we explore the design space spanned by the
orientations of the antennas in a WiNoC architecture with the goal of
improving its energy efficiency.

% ---------------------------------------------------------------------------

\subsection{Simulation Methodology}
Given the non-linear, high dimensional, multi-modal, and non-smooth
nature of $E_{ij}(\Psi)$, the optimization problems
[Eqns.~(\ref{eq:as_case})--(\ref{eq:wc_case})], defined in the
previous section, have been solved by means of simulated annealing.
\begin{eqnarray}
  \min_{\Psi} \sum_{i=0}^N \sum_{j=0}^N V_{ij} \times E_{ij}(\Psi) \label{eq:as_case} \\
  \min_{\Psi} \sum_{i=0}^N \sum_{j=0}^N E_{ij}(\Psi) \label{eq:gp_case} \\
  \min_{\Psi} \max_{i,j=1,\ldots,N} E_{ij}(\Psi) \label{eq:wc_case}
\end{eqnarray}
For each of the above scenarios, namely, application specific [AS,
  Eqn.~(\ref{eq:as_case})], general purpose [GP,
  Eqn.~(\ref{eq:gp_case})], and worst case [WC,
  Eqn.~(\ref{eq:wc_case})], the optimal set of antennas orientation,
namely, $\Psi^{(AS)}_{opt}$, $\Psi^{(GP)}_{opt}$, and $\Psi^{(WC)}_{opt}$,
are simulated by means of an accurate field solver simulator for
obtaining the scattering parameters. Then, scattering parameters are
used by Eqn.~(\ref{eq:friis_measured}) for computing the transmitting
power for each transmit-receive antenna pair. Such transmitting power
data are then used for back-annotating a cycle accurate WiNoC
simulator~\cite{winoxim} for determining the total energy figures
under different traffic scenarios.

\begin{table}
  \caption{HFSS setup parameters.}
  \label{tab:parameters}
  \centering
  \begin{tabular}{@{}lc@{}}
    \toprule
    \multicolumn{1}{c}{Parameter} & \multicolumn{1}{c}{Value} \\  
    \midrule
    Chip Size                 & $20~\mathrm{mm} \times 20 \mathrm{mm}$ \\
    Technology                & $28~\mathrm{nm~SOI}$ \\
    Silicon Resistivity       & $\rho=5~\mathrm{K \Omega cm}$ \\
    Substrate Thickness       & $350~\mathrm{\mu m}$ \\
    Oxide ($SiO_2$) Thickness & $30~\mathrm{\mu m}$ \\
    Antenna Elevation         & $2~\mathrm{\mu m}$ \\
    Antenna Thickness         & $2~\mathrm{\mu m}$ \\
    Antenna Axial Length      & $2 \times 340~\mathrm{\mu m}$ \\
    Operation frequency       & $60~\mathrm{GHz}$ \\
    Absolute Bandwidth        & $16~\mathrm{GHz}$ \\
    \bottomrule
  \end{tabular}
\end{table}
In all the experiments we consider a zigzag antenna modelled and
characterized with Ansoft HFSS~\cite{hfss} (High Frequency Structural
Simulator). HFSS produces scattering parameter and radiation pattern
as output. Tab.~\ref{tab:parameters} reports the simulation parameters
used in all the experiments.

\begin{figure}
  \centering
    \includegraphics[width=0.30\textwidth]{pictures/rpattern_phi.eps}
    \caption{Radiation pattern for a zigzag antenna at the elevation
      of maximum radiation ($\phi=100^\circ$). $\theta=0^\circ$ is the
      direction ortogonal to the antenna's main axis. According to
      Fig.~\ref{fig:friis}, we assume the antenna situated upon the XY
      plane (coplanar with silicon die).}
  \label{fig:rad_patterns}
\end{figure}
Fig.~\ref{fig:rad_patterns} shows the antenna directivity, by means of
its radiation pattern, considering the direction of maximum radiation
under the substrate ($\phi=100^\circ$).  

%% Please notice that, although
%% several effects, including, multi-path, reflections, \etc, have not
%% been modelled, the experimental setup used in this paper provides an
%% accuracy level high enough for the purpose of design space
%% exploration~\cite{tap_07,Abadal_tnet14,yu_mtt14}.

% ------------------------------------------------------------------------------

\subsection{Energy Saving Analysis}
Let us know analyse the energy savings in the application specific
(AS), general purpose (GP), and worst case (WC) scenarios. As
communication traffic patters, we used a set of representative
applications of SPLASH-2 and PARSEC benchmarks suites. Such benchmarks
have been executed on Graphite Multi-core
Simulator~\cite{miller_hpca10} and the communication topology graphs
and communication volumes information have been extracted. In all the
experiments, the baseline WiNoC architecture is
msWiNoC~\cite{deb_tc13} in which all the antennas have the same
orientation. In the case of AS and GP, it is assumed that the power
amplifier in the transceivers is equipped with the reconfigurable
variable gain amplifier (R-VGA) module~\cite{mineo_date14} with seven
power steps.  The estimated transmitting power ranges from 8~$\mu$W
(-21~dBm) to 794~$\mu$W (-1~dBm), that in terms of energy per bit
correspond to 0.42~pJ/bit and 1.4~pJ/bit, respectively. Based on this,
we have selected seven equally spaced power steps into such
range. That is, the $i$-th power step corresponds to a transmitting
power of $8 + (i-1)*786/6$ $\mu$W.

\begin{figure}
  \centering
  \includegraphics[width=0.4\textwidth]{pictures/iWise64.eps} 
  \caption{Energy saving obtained for ms-WiNoC with 256 nodes under
    different traffic scenarios.}
  \label{fig:results1}
\end{figure}
Fig.~\ref{fig:results1} shows the percentage energy saving when the
antennas are optimally oriented based on the solutions of optimization
problems [Eqns.~(\ref{eq:as_case})--(\ref{eq:wc_case})] considering
four antenna orientations steps. On average, up to 89\%, 82\%, and
78\% energy saving is observed for AS, GP, and WC scenario,
respectively.

\begin{figure}
  \centering
  \includegraphics[width=0.4\textwidth]{pictures/ms-winoc_vs_no_hubs.eps} 
  \caption{Energy saving for different number of radio hubs.}
  \label{fig:results2}
\end{figure}
Fig.~\ref{fig:results2} shows the percentage energy saving when the
number of radio hubs is made to vary. As expected, the energy saving
increases as the number of radio hubs increases due to the fact that
more communications make use of the radio medium. However, no relevant
improvement is observed when the number of radio hub is greater than
eight. Such trend is related to the network size that in our
experiments consists of 256 communicating cores. In fact, for such a
medium network size, eight radio hubs are enough for drastically
reducing the average hop count.  Above eight radio hubs, the short
distances between them, makes more suitable performing the
communication by means of the wired underlying NoC. Please remind
that, wireless transmissions becomes effective in term of energy
efficiency when the path length is greater than three
hops~\cite{daly_jssc07}. 

\begin{figure}
  \centering
  \includegraphics[width=0.40\textwidth]{pictures/ms-winoc_vs_no_or.eps} 
  \caption{Energy saving for various number of possible orientations
    of the antenna (WiNoC configured with 16 radio hubs).}
  \label{fig:results3}
\end{figure}
%% The optimal antennas orientation vector $\Psi_{opt}$, is computed
%% without any constraint on the set of physically implementable antenna
%% orientations. 
We analysed four cases in which 2, 4, 8, and 16
orientations are allowed. Such allowed orientations are those obtained
by equally dividing the orientations from $0^\circ$ to $180^\circ$ into
2, 4, 8, and 16 angles, respectively. Fig.~\ref{fig:results3} shows
the percentage energy savings in such cases. It is interesting to
observe that AS is quite insensitive to the increase of the number of
admissible antenna orientations. This behaviour is explained by the
fact that AS directs the antenna along the direction with the maximum
traffic volume. For this reason, having more than two available
orientations, does not affect the solution found for AS. On contrary,
GP and WC are strongly sensitive to the number of available antenna
orientations. As it can be observed, passing from 2 to 4 possible
orientations, it results in an energy saving gap of about 20\% and
45\% for GP and WC, respectively. For instance, in the case of GP, the
optimal orientation of the antennas is determined by assuming that the
traffic volume between all the radio hub pairs is the same. Thus, for
a generic antenna, a trade-off orientation is determined in such a way
to satisfy all the directions.

%--------------------------------------------------------------------------- 

\subsection{Case Study}
\begin{figure}
  \centering
  \includegraphics[width=0.4\textwidth]{pictures/case_study64.eps}
  \caption{Heterogeneous system composed by a multimedia sub-system, a
    MIMO-OFDM receiver, a PIP and a MWD module.}
  \label{fig:case_study64}
\end{figure}
As a real case study, we consider a complex heterogeneous platform
shown in Fig.~\ref{fig:case_study64}. The system is composed by a
generic MultiMedia System which includes a H.263 video encoder, a
H.263 video decoder, a MP3 audio encoder and a MP3 audio
decoder~\cite{hu_tcad05}, a MIMO-OFDM receiver~\cite{yoon_act06}, a
Picture-In-Picture application (PiP)~\cite{jaspers_tice99} and a
Multi-Window Display application (MWD)~\cite{vandertol_mp02}.
Fig.~\ref{fig:case_study64} shows the application mapped on a
HmWNoC~\cite{deb_tc13} partitioned in 16 subnetworks where the upper
level network is a 2D mesh topology augmented with three radio
hubs. The number of radio hubs and their placement into the network
has been derived by using the optimization procedure described
in~\cite{deb_tc13}.


\begin{figure}
  \centering
  \begin{tabular}{c}
%    AS & WC \\
    AS \\
    \includegraphics[width=0.30\textwidth]{pictures/asic_orientations.eps} \\
    \\
    WC \\
    \includegraphics[width=0.30\textwidth]{pictures/worst_case_orientations.eps}
  \end{tabular}
  \caption{Optimal antennas orientations for the application specific
    and worst case scenarios.}
  \label{fig:cs_orientation}
\end{figure}
We explore the antennas orientation design space for both the
application specific (AS) and worst case (WC) scenarios. We consider
antennas can be oriented among four angles ($0^\circ$, $45^\circ$,
$90^\circ$, $135^\circ$). We assume a tunable power amplifier
suporting seven power steps with a transmitting energy per bit ranging
from 0.42~pJ/bit to 1.4~pJ/bit. Fig.~\ref{fig:cs_orientation} shows
the optimal orientation of the three antennas for the two
scenarios. With regard to the AS scenario, due to the presence of
memory elements close to C14, which represents an hot-spot region of
the network, there is a relevant traffic volume between such region
and both C0 and C7. Based on this, as can be observed from
Fig.~\ref{fig:cs_orientation} (AS), both antennas in C7 and C0 are
oriented in such a way to reduce energy when communicate with
C14. With regard to the WC scenario, since no traffic information is
used during the design space exploration, the optimal orientation of
the antennas found, tries to minimize the worst case condition which
is represented by the communication between the two far apart
clusters, namely, C14 and C0. In fact, as it can be noticed, the
antenna in C14 fits the directivity of the antenna in C0 and
viceversa.

\begin{table}
  \centering
  \caption{Transmitting energy per bit for each transmitting and
    receiving antennas pair.}
  \label{tab:cs_energy}
  \begin{tabular}{|c|c|c|c|c|}
    \hline
       &    & \multicolumn{3}{|c|}{Transm. energy (pJ/bit)} \\
    TX & RX & BS & AS & WC \\
    \hline \hline
    C14 & C7 & 1.40 & 0.58 & 1.07 \\
    \hline
    C14 & C0 & 1.40 & 1.23 & 1.07 \\
    \hline
    C7 & C14 & 1.40 & 0.58 & 1.07 \\
    \hline
    C7 & C0 & 1.40 & 0.91 & 1.07  \\
    \hline
    C0 & C14 & 1.40 & 1.23 & 1.07 \\
    \hline
    C0 & C7 & 1.40 & 0.91 & 1.07  \\
    \hline \hline
    \multicolumn{2}{|c|}{Total energy (J)} & $1.68 \times 10^{-4}$ &
    $1.23 \times 10^{-5}$ & $1.02 \times 10^{-4}$ \\
    \hline
  \end{tabular}
\end{table}
Tab.~\ref{tab:cs_energy} reports, for each transmitting and receiving
antennas pair, and for each considered scenario, the transmitting
energy per bit. The table also shows a baseline scenario (BS) in which
all the antennas have the same orientation ($0^\circ$). Of course, for
both the WC and BS scenarios, the transmitting energy is constant
irrespective of the location of the transmitting and receiving
antenna. The optimization of the antennas orientation in the WC
scenario allows to reduce the communication energy by 39\% as respect
to the BS scenario. By considering the AS scenario, in which the
transmitting power is tuned online, the communication energy reduces
by 51\%.

%% \begin{figure}
%%   \centering
%%   \includegraphics[width=0.35\textwidth]{pictures/worst_case_orientations.eps}
%%   \caption{Antennas orientation obtained by applying application specific optimization (AS).}
%%   \label{fig:worst_case_orientation}
%% \end{figure}

%% \begin{figure}
%%   \centering
%%   \includegraphics[width=0.35\textwidth]{pictures/asic_orientations.eps}
%%   \caption{Antennas orientation obtained by applying worst case optimization (WC).}
%%   \label{fig:asic_orientation}
%% \end{figure}
%% By applying both worst case (WC) and application specific (AS) methods
%% results in the configurations shown in Fig.~\ref{fig:worst_case_orientation} 
%% and~\ref{fig:asic_orientation} respectively. In the former case, 
%% antennas configuration is independent by data traffic. In fact, antenna in C14
%% is directed in such way to minimize the worst case condition which
%% is present when cluster C14 communicates with C0.

%% Since the proposed application presents memory elements near the hub C0, 
%% both C10 and C07 need to transfer huge amount of data in that region.
%% In fact, Fig.~\ref{fig:asic_orientation} highlights that antenna in C07
%% is oriented in order to reduce energy when communicate with C10. 
%% Once again, the application of the proposed technique results in
%% interesting energy saving up to 51\% and 39\% when AC and WC methods
%% are applied respectvelly.


%% We considered the transceiver proposed in~\cite{daly_jssc07}, also
%% used in~\cite{ditommaso_hoti11}, which provides seven adjustable
%% output power steps.

%% The estimated transmitting power ranges from 8~$\mu$W (-21~dBm) to
%% 794~$\mu$W (-1~dBm), that in terms of energy per bit correspond to
%% 0.42~pJ/bit and 1.4~pJ/bit, respectively. Based on this, we have
%% selected seven equally spaced power steps into such range. Precisely,
%% the $i$-th power step is $8 + (i-1)*786/6$ $\mu$W.  For estimating the
%% overhead due to the control network, R-VGA, and the encoding/decoding
%% logic for the error detection, they have been modelled in VHDL and
%% synthesized using Synopsys Design Compiler considering a 28~nm CMOS
%% standard cell library from TSMC operating at 2~GHz (based on the
%% working frequency of the synthesized
%% router). Figs.~\ref{fig:breakdowns}(a) and~\ref{fig:breakdowns}(b)
%% show the area and power breakdown of the radio hub, respectively. Some
%% of the elements which form the radio hub (\eg, the R-VGA, the
%% \emph{CSw} of the control network, and the error control logic) depend
%% on the number of radio hubs in the networks. This is due to the fact
%% that the number of bits used for encoding the address of the radio hub
%% and the number counters in the R-VGA depend on the total number of
%% radio hubs in the network. For this reason we considered three
%% scenarios corresponding to a network in which 4, 8, and 16 radio hubs
%% are used. As it can be observed, in the worst case analyzed, the total
%% overhead for implementing the proposed scheme does not exceed 2.6\%
%% and 5\% of the radio hub area and power, respectively.  Energy figures
%% have been used for back-annotating a cycle accurate NoC simulator
%% based on Noxim~\cite{noxim} and augmented with wireless
%% communication. The attenuation map has been obtained by HFSS and used
%% as input by the simulator for the injection of errors in wireless
%% communication. Simulations have been performed considering three
%% typical WiNoC architectures, including, two mesh-based WiNoC
%% architectures, namely, McWiNoC~\cite{zhao_nocs11} and
%% iWise64~\cite{ditommaso_hoti11}, and a small-world based WiNoC,
%% namely, mSWNoC~\cite{deb_tc13}. For this latter, the optimum number
%% (twelve) and optimal location of radio hubs, computed using the
%% approach presented in~\cite{deb_tc13}, has been
%% considered. Fig.~\ref{fig:savings} shows the energy savings obtained
%% by applying the proposed technique. As it can be observed, on average,
%% the application of the proposed scheme results in an energy saving of
%% 40\%, 39\%, and 21\% for McWiNoC, iWise64, and mSWNoC, respectively.
